Structural acoustics model of the violin radiativity profile.

Violin radiativity profiles are dominated by the Helmholtz-like A0 cavity mode ( approximately 280 Hz), first corpus bending modes B1(-) and B1(+) ( approximately 500 Hz), and BH and bridge-filter peaks ( approximately 2.4 kHz and approximately 3.5 kHz, respectively), with falloff above approximately 4 kHz. The B1 modes-dependent on two low-lying free-plate modes--are proposed to excite A0 via coupling to B1-driven in-phase f-hole volume flows. VIOCADEAS data show that A0 radiativity increases primarily as A0-B1(-) frequency difference decreases, consistent with Meinel's 1937 experiment for too-thick/too-thin plate thicknesses, plus sound post removal and violin octet baritone results. The vibration-->acoustic energy filter, F(RAD), computed from shape-material-independent radiation and total damping, peaks at the critical frequency f(crit), estimated from a free-plate mode by analogy to flat-plate bending. Experimentally, f(crit) decreased as this plate mode (and B1(+)) frequency increased. Simulations show that increasing plate thicknesses lowers f(crit), reduces F(RAD), and moves the spectral balance toward lower frequencies. Incorporating string-->corpus filters (including bridge versus bridge-island impedances) provides a model for overall violin radiativity. This model-with B1 and A0-B1 couplings, and f(crit) (computed from a free-plate mode important to B1) strongly affecting the lowest and highest parts of the radiativity profile-substantiates prior empirical B1--sound quality linkages.